2x2 Design
We will begin with the simplest factorial design -- 2 x 2 ANOVA. In this design, we have two independent variables, each with two levels/groups in the study design. Remember that we describe each factor in our design by the number of levels or groups in the design.
We are examining the results of a study of eye-witness testimony. The investigators wish to know whether recall of important information is influenced by the severity of the crime and the amount of time that passes before the witness is asked to recall important events. The study is described below.
The first independent variable is severity of the crime. A videotape is made of a man stealing a woman's purse in an uncrowded clothing store. A second videotape is made, using the same actors, of a man using a gun to rob the cash register of the same clothing store. In this scenario, the woman is a sales clerk behind the cash register and there are two people standing at the counter.
The second independent variable istime to recall. Subjects are asked to view the videotape and to imagine that they are at the crime scene. In the "immediate" condition, subjects are asked a series of questions about the crime within 10 minutes of viewing the videotape. In the "delay" condition, they are asked the same series of questions about the crime 20-30 minutes after viewing the tape. This is designed to be similar to an actual crime scene where there is some delay when taking witness statements.
The dependent variable is the total number of questions answered correctly. Subjects were college students who were randomly assigned to experimental groups; 10 subjects were assigned to each group.
Go to the next page to see the general structure of this experiment and the data collected.
What is the first step in our calculations? Squaring raw data and calculating the sums of raw scores and sums of squares.
Fill in the following chart by squaring the X value in each cell of the table and adding them together. Check your answer by clicking button at the bottom of the chart.
This value is used in many of the sums of squares calculations for specific factors in the design. It draws upon the following data from the experiment. Remember that there are 10 subjects in each cell in the design.
Now that we have the relevant sums and sums of squares for our raw data (see chart below), we can continue with our sums of squares calculations for the various effects in the design.
We calculate an estimate of the grand mean that is used in many formulas, calculate an estimate for the total sums of squares, and then calculate a sums of squares estimate for each effect in the design -- main effect for Factor A (Severity of Crime), main effect for Factor B (Time of Testing) and the interaction of Factor A and Factor B (Severity x Time). Finally, we calculate the sums of squares estimate for the within-group variance, which serves as our error term.
http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/fact_anova/fact_anova_01.html
2x2 Design
We will begin with the simplest factorial design -- 2 x 2 ANOVA. In this design, we have two independent variables, each with two levels/groups in the study design. Remember that we describe each factor in our design by the number of levels or groups in the design.
We are examining the results of a study of eye-witness testimony. The investigators wish to know whether recall of important information is influenced by the severity of the crime and the amount of time that passes before the witness is asked to recall important events. The study is described below.
The first independent variable is severity of the crime. A videotape is made of a man stealing a woman's purse in an uncrowded clothing store. A second videotape is made, using the same actors, of a man using a gun to rob the cash register of the same clothing store. In this scenario, the woman is a sales clerk behind the cash register and there are two people standing at the counter.
The second independent variable is time to recall. Subjects are asked to view the videotape and to imagine that they are at the crime scene. In the "immediate" condition, subjects are asked a series of questions about the crime within 10 minutes of viewing the videotape. In the "delay" condition, they are asked the same series of questions about the crime 20-30 minutes after viewing the tape. This is designed to be similar to an actual crime scene where there is some delay when taking witness statements.
The dependent variable is the total number of questions answered correctly. Subjects were college students who were randomly assigned to experimental groups; 10 subjects were assigned to each group.
Go to the next page to see the general structure of this experiment and the data collected.
Fill in the following chart by squaring the X value in each cell of the table and adding them together. Check your answer by clicking button at the bottom of the chart.
Now that we have the relevant sums and sums of squares for our raw data (see chart below), we can continue with our sums of squares calculations for the various effects in the design.
We calculate an estimate of the grand mean that is used in many formulas, calculate an estimate for the total sums of squares, and then calculate a sums of squares estimate for each effect in the design -- main effect for Factor A (Severity of Crime), main effect for Factor B (Time of Testing) and the interaction of Factor A and Factor B (Severity x Time). Finally, we calculate the sums of squares estimate for the within-group variance, which serves as our error term.